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Mod $l$ algebraic $K$-theory of product of an algebra with a complete algebra

By Gabber's rigidity the mod-$l$ $K$-theory of $k[[t]]$ and $k$ are isomorphic for a field $k$. Is there anything that we can say about the mod $l$ $K$-theory of $A\otimes_kk[[t]]$? Note that this is ...
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Poincaré duality for motivic cohomology

Is Poincaré duality for étale motivic cohomology known for projective regular (not necessarily smooth, just regular) schemes over Dedekind rings? More precisely, two questions. Let $f: \mathcal{X}\to\...
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